Question

classes 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 15.5 m/s2 for a time period of 3.50 s. after this time period, the rocket engine abruptly shuts off, and the sled subsequently undergoes a constant backward acceleration due to friction of 5.65 m/s2. after the rocket turns off, how much time does it take for the sled to come to a stop? time: 9.60 s by the time the sled finally comes to a rest, how far has it traveled from its starting point? distance traveled: 247.73

Answer 1

Step-by-step explanation:

Given:

a₁ = 15.5 m/s²

t₁ = 3.50 s

a₂ = -5.65 m/s²

v₂(t=3.5) = a₁t₁

= 15.5 × 3.5

= 54.25 m/s

v₃(rocket stop) = 0

v₂ + a₂t₂ = 0

54.25 + (-5.65)t₂ = 0

t₂ = 54.25 ÷ 5.65

= 9.60 s

s = s(0 ≤ t ≤ 3.5) + s(3.5 ≤ t ≤ 9.60)

= v₀t₁ +
`(1)/(2)`a₁t₁² + v₂t₂ +
`(1)/(2)`a₂t₂²

= 0 +
`(1)/(2)`(15.5)(3.5)² + (54.25)(9.60) +
`(1)/(2)`(-5.65)(9.60)²

= 94.9375 + 520.8 - 260.352

= 355.39 m