A runner, beginning from x = 0 and t = 0, accelerates at a constant rate for 10 seconds and reaches a speed of 8 m/sec. The runner maintains that speed  until he reaches x = 100 m. Find t100, the time at which the runner reaches 100 m. Explain your approach and assumptions.

A particle moving along the x axis has acceleration in the x direction as function of the time given by a(t) = 6t²-t. For t=0 the initial velocity is 6.0 m/s. Determine the velocity when t = 1.0 s. Write here your answer. Include the units.

A car starts from rest with an acceleration of 5.3 m/s² which decreases linearly with time to zero in 10.3 seconds, after which the car continues at a constant speed. Determine the time t required for the car to travel 330 m from the start. Answer: t = i ! S

A woman backs her van out of her parking space with a constant acceleration of 1.8 m/s2. Assume that her initial motion is in the positive direction. Part A: How long does it take her to reach a speed of 2.1 m/s in seconds?  Part B: If she then brakes to a stop in 0.65 s, what is her acceleration in meters per square second?

A car starts from rest. It accelerates at constant acceleration for 5.0 seconds during which the car covers a distance of 125 m. After that the car continues at that speed for 22 seconds, after which the car slows down at a constant deceleration of – 4.5 m/sec2 until coming to a complete stop. Draw a v vs t, graph, label all the relevant data, and use the graphical method to determine total distance traveled.

A driver is driving uphill. He maintained his throttle, causing his car to constantly decelerate as it is coming up the hill. The road going up the hill is 217 m long and it took him 8.8 seconds to get to the top of the hill. His speed has reduced to 22 m/s at that point. What was the car's acceleration (include a negative sign in your answer)? Hint: the initial position of the car can be set at the origin.

A cheetah can reach the top speed of 114 km/h. A cheetah starts from rest and runs 48 m in a straight line, reaching a final speed of 94 km/h. 1. what's the average acceleration during sprint (m/s^2) 2. find displacment at t=3.0 s assuming constant acceleration throughout sprint

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 6.25 m/s. The car is a distance d away. The bear is 21.3 m behind the tourist and running at 8.64 m/s. The tourist reaches the car safely. What is the maximum possible value for d? Vbear Number i Vtourist Units

Here, you derive the formula. At t = 0, a car is going v0 and is x0 from the start of the road.  The driver accelerates the car at a until time t.  Derive the formula for x(t).

A group of students in a science class monitored the movement of a cat walking along with a straight line and recorded the cat's position in five-second intervals.The results are summarized it in the table below.  time and position time(s) position (cm) 0 49.0 5 38.0 10 43.0 15 40.0 20 60.0   A. What is the displacement of the cat between t = 5.00 s and t = 20.0 s?   B. What is the average velocity of the cat between t = 5.00 s and t = 20.0 s?   C.What is the distance the cat traveled between t = 5.00 s and t = 20.0 s?