A drag racer starting from rest accelerates in a straight line at a constant rate of 5.5 m/s2 for 6.0 s. After this, a parachute deployed causes the racer to slow down uniformly at a rate of 2.4 m/s2. How long will it take the racer to come to a stop?
To answer this question, we need to consider two phases of motion: the acceleration phase and the deceleration phase.
In the acceleration phase, we are given that the drag racer starts from rest and accelerates at a constant rate of 5.5 m/s² for 6.0 seconds. We can use the equation of motion:
v = u + at
where:
v = final velocity
u = initial velocity (which is zero in this case)
a = acceleration
t = time
Plugging in the values, we have:
v = 0 + (5.5 m/s²)(6.0 s)
v = 33 m/s
Therefore, the drag racer reaches a speed of 33 m/s after 6.0 seconds of acceleration.
In the deceleration phase, the parachute is deployed, causing the racer to slow down uniformly at a rate of 2.4 m/s². We want to find the time it takes for the racer to come to a stop, so we need to find the time it takes for the final velocity to become zero.
Using the same equation of motion, but with a negative acceleration (deceleration in this case), we have:
v = u + at
where:
v = final velocity (zero in this case)
u = initial velocity (33 m/s)
a = deceleration (-2.4 m/s²)
t = time
Plugging in the values, we have:
0 = 33 m/s + (-2.4 m/s²)(t)
-33 m/s = -2.4 m/s²(t)
t = -33 m/s / -2.4 m/s²
t ≈ 13.75 s
Therefore, it will take approximately 13.75 seconds for the racer to come to a stop after the parachute is deployed.