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

Answer:

The value of t₁ is 5.119 sec.

Explanation:

Given that,

Acceleration = 12.7 m/s²

Total distance $D=5.85\times10^{3}\ m$

Time = 94.6 sec

We need to calculate the distance

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

Put the value into the formula

$s_{1}=0+\dfrac{1}{2}12.7t_{1}^2$...(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

$s_{1}+s_{2}=5.85\times10^{3}$

Put the value of s₁ and s₂

$\dfrac{1}{2}12.7t_{1}^2+12.7t_{1}t_{2}=5.85\times10^{3}$

$6.35t_{1}+12.7t_{1}t_{2}=5.85\times10^{3}$...(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.