Question

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 12.8 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 5.37 × 103 m and the total time is 97.7 s. Find t1.

Answer 1

Answer:4.39 s

Step-by-step explanation:

Given

initial velocity
`u=0`

acceleration
`a=12.8 m/s^2`

velocity acquired by sled in
`t_1` time

`v=0+at`

`v=12.8t_1`

distance traveled by sled in
`t_1 s`

`v^2-u^2=2as`

`(12.8t_1)^2-0=2* 12.8* s_1`

`s_1=6.4\cdot t_1^2`

distance traveled in
`t_2` time with velocity
`v=12.8t_1`

`s_2=v* t_2`

`s_2=12.8* t_1* t_2`

`s_2=12.8\cdot t_1\cdot t_2`

`s_1+s_2=5.37* 10^3`

`6.4t_1^2+12.8t_1t_2=5370`----1

`t_1+t_2=97.7 s`

`t_2=97.7-t_1`

substitute the value of
`t_2` in 1

we get

`6.4t_1^2-1250.56t_1+5370=0`

thus
`t_1=(1250.56-1194.33)/(12.8)=4.39 s`

`t_1=4.39 s`