Question

A car starting from rest accelerates at a rate of $8.0{\text{ }}\dfrac{m}{{{s^2}}}$. What is its final speed at the end at $4.0$ seconds?

Answer 1

It is given in the question that a car starts from rest and the acceleration of the car is $8.0{\text{ }}\dfrac{m}{{{s^2}}}$. We have to find the velocity of the car at $4.0$ seconds. By using the motion’s equation and substituting the values of the variables we will find the answer. Since, the car starts from rest. So, its initial velocity is zero.

Complete step by step solution:
It is given in the question that a car starts from rest and the acceleration of the car is $8.0{\text{ }}\dfrac{m}{{{s^2}}}$. We have to find the velocity of the car at $4.0$ seconds.
Since, the car starts from rest. So, its initial velocity is zero.
Let us consider that the initial velocity of the car be $u$ and the final velocity of the car after $4.0$ seconds be $v$.
We have to find the final velocity of the car with the help of motion’s equation.
From the motion’s equation we get,
$v = u + at - - - - - \left( 1 \right)$
The variables are defined as,
$v =$ final velocity of any object
$u =$ initial velocity of any object
$a =$ acceleration of any object
$t =$ time
From the given question we get, the initial velocity $u = 0$, time $t = 4$ and the acceleration of the particle $a = 8$.
Substituting the values in the given equation $\left( 1 \right)$ we get,
$v = 0 + 8 \times 4 = 32$
Therefore, the final velocity of the after $4.0$ seconds is $32{\text{ }}\dfrac{m}{s}$.

Note:
It must be noted that the initial velocity of the particle is zero as the particle starts from the position of rest. Acceleration of a particle is defined as the time rate of change of velocity. The particle here is in accelerated motion as its velocity is increasing.