Concept explainers
Based on observations, the speed of a jogger can be approximated by the relation
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Vector Mechanics For Engineers
- In anticipation of a long 7° upgrade, a bus driver accelerates at a constant rate of 3 ft/s2 while still on a level section of the highway. Knowing that the speed of the bus is 60 mi/h as it begins to climb the grade and that the driver does not change the setting of his throttle or shift gears, determine the distance traveled by the bus up the grade when its speed has decreased to 50 mi/h.arrow_forwardThe brakes of a car are applied, causing it to slow down at a rate of 10 ft/s2 . Knowing that the car stops in 300 ft, determine (a) how fast the car was traveling immediately before the brakes were applied, (b) the time required for the car to stop.arrow_forwardA ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5 ft/s. While in the water the ball experiences an acceleration of a = 10 − 0.8v, where a and v are expressed in ft/s2 and ft/s, respectively. Knowing that the ball takes 3 s to reach the bottom of the lake, determine (a) the depth of the lake, (b) the speed of the ball when it hits the bottom of the lake.arrow_forward
- A ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5 ft/s. While in the water the ball experiences an acceleration of a = 10 − 0.8v, where a and v are expressed in ft/s2 and ft/s, respectively. Knowing that the ball takes 3 s to reach the bottom of the lake, determine the speed of the ball when it hits the bottom of the lake.arrow_forwardThe acceleration of a particle is defined by the relation a = –kv^2.5, where k is a constant. The particle starts at x = 0 with a velocity of 16 mm/s, and when x = 14 mm, the velocity is observed to be 8 mm/s. Determine the velocity of the particle when x = 5 mm. in mm/sarrow_forwardAssuming a uniform acceleration of 11 ft/s2 and knowing that the speed of a car as it passes A is 30 mi/h, determine (a) the time required for the car to reach B, (b) the speed of the car as it passes B.arrow_forward
- Jack run on a marathon with a speed that can be approximated by the relation v= 6.5(1.2 - 0.05x) ^ 0.3, where v and x are expressed in mi/h and miles respectively. Knowing that x= 0 at t = 0, determine (a.) the distance Jack has run when t =1h, (b) Jack's acceleration in ft/s^2 at t=0, (c.) the time required for him to run 6 mi. helppparrow_forwardCar A is traveling at 40 mi/h when it enters a 30 mi/h speed zone. The driver of car A decelerates at a rate of 16 ft/s2 until reaching a speed of 30 mi/h, which she then maintains. When car B , which was initially 60 ft behind car A and traveling at a constant speed of 45 mi/h, enters the speed zone, its driver decelerates at a rate of 20 ft/s2 until reaching a speed of 28 mi/h. Knowing that the driver of car B maintains a speed of 28 mi/h, determine (a) the closest that car B comes to car A, (b) the time at which car A is 70 ft in front of car B.arrow_forwardThe motion of a particle is defined by the relation x = 2t^3 – 15t^2+24t +4, where xis expressed in meters and t in seconds. Determine (a) when the velocity is zero, (b) the positionand the total distance travelled when the acceleration is zero.arrow_forward
- A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the slope, GPS coordinates are used to determine her displacement as a function of time: x = 0.5t^3 + t^2 + 2t, where x and t are expressed in feet and seconds, respectively. x is measured along the surface of the hill. Determine the position, velocity, and acceleration of the boarder when t = 5 seconds. (x=___ft; v=___ft/s; a=___ft/s^2arrow_forwardTwo road rally checkpoints A and B are located on the same highway and are 8 mi apart. The speed limits for the first 5 mi and the last 3 mi are 60 mi/h and 35 mi/h, respectively. Drivers must stop at each checkpoint, and the specified time between points A and B is 10 min 20 s. Knowing that the driver accelerates and decelerates at the same constant rate, determine the magnitude of her acceleration if she travels at the speed limit as much as possible.arrow_forwardThe brakes of a car are applied, causing it to slow down at a rate of 10 m/s^2. Knowing that the car stops in 300 m, determine (a) how fast the car was traveling immediately before the brakes were applied.arrow_forward
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