A car traveling east at 42.4 m/s passes a trooper hiding at the roadside. The driver uniformly reduces his speed to 25.0 m/s in 4.00 s.
(a) What is the magnitude and direction of the car's acceleration as it slows down?
initial velocity = 42.4 m/s
final velocity = 25.0 m/s
time = 4.00s
a =
(final velocity - initial velocity)/time
(25.0m/s - 42.4m/s)/ 4.00 s
'sign' of answer determines direction of acceleration
North
To find the magnitude and direction of the car's acceleration as it slows down, we need to use the equation for acceleration:
Acceleration (a) = (final velocity - initial velocity) / time
In this case, the initial velocity of the car is 42.4 m/s (traveling east), and the final velocity is 25.0 m/s (still traveling east). The time taken for this change in velocity is 4.00 seconds.
Calculating the acceleration:
a = (25.0 m/s - 42.4 m/s) / 4.00 s
a = (-17.4 m/s) / 4.00 s
a = -4.35 m/s²
Therefore, the magnitude of the car's acceleration as it slows down is 4.35 m/s². The negative sign indicates that the direction of the acceleration is opposite to the initial velocity, so it is also traveling east.