Question

Help me find the acceleration

Answer 1

a = 3.09 m/s²

Step-by-step 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 = (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 = (v^(2) - u^(2))/(2\; x)\\\phantom{a} = ((-10.9)^(2) - (-27.7)^(2))/(2 * (-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.