Question

USE K U E S
Problem 1.
A runner accelerates to 4.2 m/s2 for 100 seconds before winning the race. How far did he/she run?

Problem 2.
A plane starts from rest and accelerates uniformly over a time of 25 s for a distance of 300 m. Determine the plane’s acceleration.

Problem 3.
A ball free falls from the top of the roof for 5 seconds. How far did it fall? What is its final velocity at the end of 5 seconds?​

Answer 1

Explanation:

Problem 1.

Initial speed of the runner, u = 0

Acceleration of the runner, $a=4.2\ m/s^2$

Time taken, t = 100 s

Let v is the speed of the runner now. Using the first equation of kinematics as :

$v=u+at$

$v=at$

$v=4.2\ m/s^2\times 100\ s$

v = 420 m/s

Problem 2.

Initial speed of the plane, u = 0

Distance covered, d = 300 m

Time taken, t = 25 s

Using the equation of kinematics as :

$d=ut+\dfrac{1}{2}at^2$

$d=\dfrac{1}{2}at^2$

$a=\dfrac{2d}{t^2}$

$a=\dfrac{2\times 300\ m}{(25\ s)^2}$

$a=0.96\ m/s^2$

Problem 3.

A ball free falls from the top of the roof for 5 seconds. Let it will fall at a distance of d. It is given by :

$d=ut+\dfrac{1}{2}gt^2$

$d=\dfrac{1}{2}\times 9.8\times (5)^2$

d = 122.5 meters

Let v is the final speed at the end of 5 seconds. Again using first equation of kinematics as :

$v=u+gt$

$v=9.8\ m/s^2\times 5\ s$

v = 49 m/s

Hence, this is the required solution.