What is the final speed of a bicyclist initially moving at 1.0 m/s who accelerates at a rate of 1.5 m/s² for 3.0 seconds?

A car is traveling along a straight road at a velocity of +39.5 m/s when its engine cuts out. For the next 2.81 seconds, the car slows down, and its average acceleration is a,. For the next 5.65 seconds, the car slows down further, and its average acceleration is ₂. The velocity of the car at the end of the 8.46-second period is +28.6 m/s. The ratio of the average acceleration values is ā,/₂ = 1.78. Find the velocity of the car at the end of the initial 2.81-second interval. 2

A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0 m/s2 until it reaches a speed of 1.50E2 m/s when the engines are cut off. After that, the rocket is in free-fall. What is the maximum height reached by the rocket?

A runner of mass 50.1 kg stařts from rest and accelerates with a constant acceleration of 1.1 m/s2 until she reaches a velocity of 6.5 m/s. She then continues running at this constant velocity. How long in seconds does the runner take to travel 104 m? 载

A car starts from rest, then accelerates at a constant rate over a distance of 80 m. It then immediately decelerates at a constant rate over a distance of 136 m. The entire trip lasts a total duration of 26.0 s. What were the magnitudes of the cars accelerations for the speedup and slowdown stages respectively?

A boy runs for 24 seconds.  During the first 8 seconds, his minimum speed is 2.6 m/s, while his maximum speed is 4.8 m/s.  During the remaining time, his minimum speed is 4.8 m/s, while his maximum speed is 5.6 m/s. calculate the maximum (least upper bound) on the distance that he runs, in meters.

A cheetah at rest notices a gazelle standing at a distance of 150.0 m. At the same time the gazelle notices the cheetah. The gazelle accelerates at 2.0 m/s2 for 8.0 s, after which it has reached top speed. The cheetah accelerates at 2.5 m/s2 until it has reached its top speed of 115.2 km/h. It can only continue at this speed for 35 s. Will the cheetah catch the gazelle? If so, when and where?

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.36 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate. Hardwood floor magnitude  m/s2 duration  ms Carpeted floor magnitude  m/s2 duration  ms

A teenager has a car that speeds up at 3.00 m/s² and slows down at - 4.50 m/s². On a trip to the store, he ac- celerates from rest to 12.0 m/s, drives at a constant speed for 5.00 s, and then comes to a momentary stop at an intersection. He then accelerates to 18.0 m/s, drives at a constant speed for 20.0 s, slows down for 2.67 s, continues for 4.00 s at this speed, and then comes to a stop. (a) How long does the trip take? (b) How far has he traveled? (c) What is his average speed for the trip? (d) How long would it take to walk to the store and back if he walks at 1.50 m/s?

A police car gets passed by a car traveling at a constant speed of 150.0 km/hr.  The police car accelerates from rest at 5.00 m/s2, the moment the two cars are side by side.  How long does it take the police officer to catch the car?