Question

When brakes are applied the velocity of a car changes from 30 $m{{s}^{-1}}$ to 10$m{{s}^{-1}}$ in 5 seconds. The acceleration produced in it is…
a) 4
b) -4
c) 20
d) -20

Answer 1

We have given the initial and final speed and the duration of time. So we can apply the equation of motion in this equation. There are three equations of motion and we have to find the suitable one for it. We have to find the acceleration when initial and final velocity is given with time. Hence we will use $v=u+at$

Formula used:
$v=u+at$

Complete Step by Step Solution:
First, we need to write the given quantities,
We have been given with initial velocity (u) = 30 $m{{s}^{-1}}$
Final velocity (v) = 10$m{{s}^{-1}}$
Time: 5 seconds
And we need to find the acceleration (a)

So we will use $v=u+at$……………………………..(1)
Where (v) is the final velocity and (u) is the initial velocity. And (t) is the time taken and (a) is the acceleration.

Put all the values in equation 1
$v=u+at$
$10=30+a\times 5$
$10-30=5a$
$-20=5a$
$a=-4m{{s}^{-2}}$

Here, the negative sign indicates that the car is de-accelerating and we know that we have given in the question that brakes are applied so the car will definitely de-accelerate and our answer is correct.

So. The solution for the above question is that the car will de accelerate at the rate of $-4m{{s}^{-2}}$.

We can conclude that option (b) is the correct answer.

Note:
When we are given with an initial velocity(u) and final velocity(v) with a time(t) and we are asked about the acceleration then the only formula that satisfies our need is $v=u+at$ because in this formula we are given with three quantities and has been asked for the fourth one. In other equations of motion we have either 5 variables or we do not have the combination for these three given quantities.