In a collision, an automobile of mass 826 kg stops with constant acceleration in 20 m from an initial speed of 17 m/s.
What is the acceleration of the car in m/s
a = (V^2-V0^2)/2d
a = (0-17^2)/40 = - 7.23 m/s^2.
To find the acceleration of the car, we can use the following formula:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) is the final velocity (which in this case is 0 m/s, since the car stops)
- \( u \) is the initial velocity (17 m/s)
- \( a \) is the acceleration that we are trying to find
- \( s \) is the distance traveled (20 m)
Rearranging the formula, we get:
\[ a = \frac{{v^2 - u^2}}{{2s}} \]
Substituting the known values into the formula:
\[ a = \frac{{0^2 - (17^2)}}{{2 \times 20}} \]
Simplifying:
\[ a = \frac{{-289}}{{40}} \]
Therefore, the acceleration of the car is approximately -7.23 m/s². Note that the negative sign indicates that the acceleration is in the opposite direction to the initial velocity.