Complete Question:
A drag racer accelerates from rest at an average rate of +13.2 m/s² for a distance of 100. m. The driver coasts for 0.5 s then uses the brakes and parachute to decelerate until the end of the track. If the total length of the track is 180 m, what minimum deceleration rate must the racer have in order to stop prior to the the end of the track?
Answer:
-31.92 m/s²
Explanation:
The drag races do a retiling uniform variated movement. There are 3 steps in the movement, first, it accelerates from rest until 100 m, second it coasts to 0.5 s, and then it decelerates. So, let's analyze each one of the steps:
Step 1
The initial velocity is v0 = 0 (because it was at rest), the acceleration is +13.2 m/s², and the distance ΔS = 100.0 m, so the final velocity, v, is:
v² = v0² + 2aΔS
v² = 2*13.2*100
v² = 2640
v = √2640
v = 51.38 m/s
Step 2
Know it's initial velocity is 51.38 m/s, it take 0.5s, and has the same acceleration, so, after 0.5 s, the velocity will be:
v = v0 + at
v = 51.38 + 13.2*0.5
v = 57.98 m/s
Thus, the distance it travels is:
v² = v0² + 2aΔS
57.98² = 51.38² + 2*13.2*ΔS
3361.6804 = 2639.9044 + 26.4ΔS
26.4ΔS = 721.776
ΔS = 27.34 m
Step 3
The initial velocity of the drag racer is 57.98 m/s, and it travels the final distance of the track: 180 - 100 - 27.34 = 52.66 m. So, when it stops, its final velocity will be 0. The minimum deceleration must be the one that it would stop at the end of the track (less than that it would cross the final track):
v² = v0² + 2aΔS
0 = 57.98² + 2a*52.66
-105.32a = 3361.6804
a = - 31.92 m/s²
