Question

lasses are canceled due to snow, so you take advantage of the extra time to conduct some physics experiments. You fasten a large toy rocket to the back of a sled and take the modified sled to a large, flat, snowy field. You ignite the rocket and observe that the sled accelerates from rest in the forward direction at a rate of 12.512.5 m/s2 for a time period of 3.303.30 s. After this time period, the rocket engine abruptly shuts off, and the sled subsequently undergoes a constant backward acceleration due to friction of 5.655.65 m/s2. After the rocket turns off, how much time does it take for the sled to come to a stop?

Answer 1

t = 7.3 s

Step-by-step explanation:

First we consider accelerated motion and use first equation of motion:

Vf = Vi + at

where,

Vf = Final Velocity = ?

Vi = Initial Velocity = 0 m/s

a = acceleration = 12.5 m/s²

t = time for acceleration = 3.3 s

Therefore,

Vf = 0 m/s + (12.5 m/s²)(3.3 s)

Vf = 41.25 m/s

Now, we consider the decelerated motion and use first equation of motion again:

Vf = Final Velocity = 0 m/s (since, sled will finally stop)

Vi = Initial Velocity = Vf of accelerated motion = 41.25 m/s

a = deceleration = -5.65 m/s²

t = time taken to stop = ?

Therefore,

0 m/s = 41.25 m/s + (-5.65 m/s²)t

t = (41.25 m/s)/(5.65 m/s²)

t = 7.3 s