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- A truck traveling along a straight, level road at 45 miles per hour when the driver is forced to apply the brakes to avoid an accident. If the brakes supply a constant deceleration of 22 ft/s2, determine: the expressions for the truck’s velocity v and position c at anytime t how long will it take to stop? how far does the car travel before coming to a complete stop?A race car travels northward on a straight, level track at a constant speed, traveling 0.587 km in 13.1 sec. The return trip over the same track is made in 27.3 sec.(a) What is the average velocity of the car for the FIRST leg of the trip?(b) What is the average velocity of the car for the SECOND leg of the trip?(c) What is the average velocity of the car for the WHOLE trip?An airplane maintains a speed of 630 km/h relative to theair it is flying through, as it makes a trip to a city 750 km awayto the north. (a) What time interval is required for the tripif the plane flies through a headwind blowing at 35.0 km/htoward the south? (b) What time interval is required if thereis a tailwind with the same speed? (c) What time interval isrequired if there is a crosswind blowing at 35.0 km/h to theeast relative to the ground?
- On a one lane road, a person driving a car at v1 = 76 mi/h suddenly notices a truck d = 1.9 mi in front of him. That truck is moving in the same direction at v2 = 45 mi/h. In order to avoid a collision, the person has to reduce the speed of his car to v2 during time interval Δt. The smallest acceleration required for the car to avoid a collision is a. During this problem, assume the direction of motion of the car is the positive direction. Refer to the figure below. a)Enter an expression, in terms of defined quantities, for the distance, Δx2, traveled by the truck during the time interval Δt. b)Enter an expression for the distance, Δx1, traveled by the car in terms of v1, v2 and a. c)Enter an expression for the acceleration of the car, a, in terms of v1, v2, and Δt. d)Enter an expression for Δx1 in terms of Δx2 and d when the driver just barely avoids collision. e)Enter an expression for Δx1 in terms of v1, v2, and Δt. f)Enter an expression for Δt in terms of d, v1, and v2. g)…A truck traveling along a straight ,level road at 45 miles per hour when the driver is forced toapply the brakes to avoid an accident. If the brakes supply a constant deceleration of 22 ft/s2,determinea.) the expressions for the truck’s velocity v and position c at anytime tb.) how long will it take to stop?c.) how far does the car travel before coming to a complete stop?ANS.:a.) v(t) = 66 – 22t and s(t) = 66t – 11t2 ; b.) 3 sec. ; c.) 99a car traveling at a constant speed of 30.0m / s as it passes a stationary police car. If the police car takes 1.00s to start, a) what must be the magnitude of the constant acceleration of the police car to intercept the car if the police travel a distance of 300m? and b) How long does the police take to reach the car?
- Car A is parked along the northbound lane of a highway, and car B is traveling in the southbound lane at a constant speed of 60 mi/h. At t=0, A starts and accelerates at a constant rate a A , while at t= 5 s, B begins to slow down with a constant deceleration of magnitude a A 6. Knowing that when the cars pass each other x = 294 ft and VA = VB , determine (a) the acceleration aA,(b) when the vehicles pass each other, (c) the distance d between the vehicles at t=0.A taxi traveling along a straight section of road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 28.0 m/s. Then the vehicle travels for 61.0 s at constant speed until the brakes are applied, stopping the vehicle in a uniform manner in an additional 5.00 s. (A) How long is the taxi in motion (in s)? Answer: 80 seconds (B) What is the average velocity of the taxi for the motion described? (Enter the magnitude in m/s.) ___________________m/sLet s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line, where t is in seconds and s is in meters. a) Determine the interval when the car is moving to the left. b) Determine the car’s position relative to the origin at the instant if the acceleration is 4 m/s^2 . c) When is the car’s acceleration positive? d) Determine if the speed of the car is increasing or decreasing at t = 4.5 seconds? e) When is the car’s acceleration negative? f) Calculate for the total distance traveled by the car during the first 5 seconds.
- On a one lane road, a person driving a car at v1 = 54 mi/h suddenly notices a truck 0.65 mi in front of him. That truck is moving in the same direction at v2 = 35 mi/h. In order to avoid a collision, the person has to reduce the speed of his car tov2 during time interval Δt. The smallest magnitude of acceleration required for the car to avoid a collision is a. During this problem, assume the direction of motion of the car is the positive direction. Refer to the figure. Part (a) Enter an expression, in terms of defined quantities, for the distance, Δx2, traveled by the truck during the time interval Δt. Part (b) Enter an expression for the distance, Δx1, traveled by the car in terms of v1, v2 and a. Part (c) Enter an expression for the acceleration of the car, a, in terms of v1, v2, and Δt.On a one lane road, a person driving a car at v1 = 54 mi/h suddenly notices a truck 0.65 mi in front of him. That truck is moving in the same direction at v2 = 35 mi/h. In order to avoid a collision, the person has to reduce the speed of his car tov2 during time interval Δt. The smallest magnitude of acceleration required for the car to avoid a collision is a. During this problem, assume the direction of motion of the car is the positive direction. Refer to the figure. The expression, in terms of defined quantities, for the distance, Δx2, traveled by the truck during the time interval Δt is deltax2= v2 times delta t. Part (b) Enter an expression for the distance, Δx1, traveled by the car in terms of v1, v2 and a. Part (c) Enter an expression for the acceleration of the car, a, in terms of v1, v2, and Δt. (d) enter an expression for delta x1 in terms of delta x2 and d when the drive just barely avoids collision.A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 175 mi/h in 2.50 s. (a) Find the average acceleration of the plane. (b) Modeling the acceleration as constant, find the distance the plane moves in this time interval.