Question

Help me find the acceleration

Answer 1

a = 3.09 m/s²

Explanation

This question doesn't tell anything about how long it took for the car to go through 105 meters. As a result, the timeless suvat equation is likely what you need for this question.

In the timeless suvat equation,

$a = \dfrac{v^2 - u^2}{2\; x}$

where

• $a$ is the acceleration of the car;
• $v$ is the final velocity of the car;
• $u$ is the initial velocity of the car; and
• $x$ is the displacement of the car.

Note that v and u are velocities. Make sure that you include their signs in the calculation.

In this question,

• $a$ is the unknown;
• $v = -10.9 \; \text{m} \cdot \text{s}^{-2}$;
• $u = -27.7 \; \text{m} \cdot \text{s}^{-2}$; and
• $x = - 105 \; \text{m}$.

Apply the timeless suvat equation:

$a = \dfrac{v^{2} - u^{2}}{2\; x}\\\phantom{a} = \dfrac{(-10.9)^{2} - (-27.7)^{2}}{2 \times (-105)}\\\phantom{a} = 3.09 \; \text{m} \cdot \text{s}^{-2}$.

The value of $a$ is greater than zero, which is reasonable. Velocity of the car is negative, meaning that the car is moving backward. The car now moves to the back at a slower speed. Effectively it accelerates to the front. Its acceleration shall thus be positive.