Question

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 12.7 m/s2 . At t1 the rocket engine is shut down and the sled moves with constant velocity v for another t2 s. The total distance traveled by the sled is 5.85 × 103 m and the total time is 94.6 s. Find t1. Answer in units of s.

Answer 1

The value of t₁ is 5.119 sec.

Step-by-step explanation:

Given that,

Acceleration = 12.7 m/s²

Total distance
`D=5.85*10^(3)\ m`

Time = 94.6 sec

We need to calculate the distance

Using equation of motion

`s=ut+(1)/(2)at^2`

Put the value into the formula

`s_(1)=0+(1)/(2)12.7t_(1)^2`...(I)

We need to calculate the velocity

Using equation of motion

`v=u+at`

Put the value into the formula

`v=0+12.7t_(1)`

`v=12.7t_(1)`

The sled while moves with constant velocity v for time t₂

Using formula of distance

`s_(2)=vt_(2)`

`s_(2)=12.7t_(1)t_(2)`

The total distance is

`s_(1)+s_(2)=5.85*10^(3)`

Put the value of s₁ and s₂

`(1)/(2)12.7t_(1)^2+12.7t_(1)t_(2)=5.85*10^(3)`

`6.35t_(1)+12.7t_(1)t_(2)=5.85*10^(3)`...(II)

The total time is

`t_(1)+t_(2)=94.6`....(III)

From equation (II) and (III)

After solving

`t_(1)=5.119\ sec`

Hence, The value of t₁ is 5.119 sec.