A car is moving at a constant velocity when it is involved in a collision.the car comes to rest after 0.45sec with an average acceleration of 65,0 m/s2 in the direction opposite that of the car's velocity. What was the speed ,in km/h, of the car before the collision?
To find the initial speed of the car before the collision, we can use the concept of average acceleration and the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given:
Acceleration (a) = -65.0 m/s^2 (since it is in the opposite direction)
Time (t) = 0.45 sec
To find the final velocity, we can use the formula v = u + at.
Since the car comes to rest (v = 0) after the collision, the equation becomes:
0 = u + (-65.0 m/s^2)(0.45 sec)
Rearranging the equation to solve for u:
u = (-65.0 m/s^2)(0.45 sec)
u = -29.25 m/s (since velocity is a vector, it has both magnitude and direction)
Now, to convert the velocity from meters per second (m/s) to kilometers per hour (km/h):
1 m/s = 3.6 km/h
u = (-29.25 m/s) * (3.6 km/h/1 m/s)
u = -105.3 km/h
Since the velocity is in the opposite direction, we take the absolute value to get the speed:
Speed before the collision = |-105.3 km/h|
Speed before the collision = 105.3 km/h
Therefore, the speed of the car before the collision was 105.3 km/h.