Question

Suppose your car accelerates from rest to 9 m/s in 2 s. Assume that the acceleration is constant in this time interval. A. What is the acceleration of your car? Express your answer in m/s 2 . B. How far will you travel in 2 s? Express your answer in meters.

Answer 1

Answer :

(a) The acceleration of the car is, $4.5m/s^2$

(b) The distance covered by the car is, 9 m

Explanation :  

By the 1st equation of motion,

$v=u+at$ ...........(1)

where,

v = final velocity = 9 m/s

u = initial velocity  = 0 m/s

t = time = 2 s

a = acceleration of the car = ?

Now put all the given values in the above equation 1, we get:

$9m/s=0m/s+a\times (2s)$

$a=4.5m/s^2$

The acceleration of the car is, $4.5m/s^2$

By the 2nd equation of motion,

$s=ut+\frac{1}{2}at^2$ ...........(2)

where,

s = distance covered by the car = ?

u = initial velocity  = 0 m/s

t = time = 2 s

a = acceleration  of the car = $4.5m/s^2$

Now put all the given values in the above equation 2, we get:

$s=(0m/s)\times (2s)+\frac{1}{2}\times (4.5m/s^2)\times (2s)^2$

By solving the term, we get:

$s=9m$

The distance covered by the car is, 9 m