Copyright

A rocket sled begins from rest. In the first 3 s, it goes 100 m at a constant acceleration. \\ a)...

Question:

A rocket sled begins from rest. In the first 3 s, it goes 100 m at a constant acceleration.

a) What is the velocity at the end of the first 3 s?

b) What was the acceleration?

c) If the maximum velocity of the rocket sled is 290 {eq}\frac{m}{s}{/eq}, how long does it take to reach that velocity?

d) How far does the rocket sled go in that amount of time?

Kinematics Equation

The kinematics equation are the set of equations used for motion of a object with uniform/constant acceleration. Few such equations are, {eq}v_f = v_i +at \\ x = (\dfrac{v_f+v_i}{2})t {/eq}, where

  • x is the displacement
  • t is the time interval
  • {eq}v_i {/eq} and {eq}v_f {/eq} are the initial and final velocity of the particles.

Answer and Explanation: 1


Given :

The initial velocity of the rocket is, {eq}v_i = 0 {/eq}

The displacement of the rocket in 3 s is, x = 100 m

The time interval of the motion is, t = 3 s


Part (a)

Let the final velocity of rocket be, {eq}v_f {/eq}

Applying the kinematics equation, we get, $$\begin{align*} x &= (\dfrac{v_f+v_i}{2})t \\ 100 &= (\dfrac{v_f+0}{2})3 \\ v_f &= 66.67 \ \frac{m}{s} \end{align*} $$


Part (b)

Let the acceleration of the rocket be, a

Applying the kinematics equation, we get, $$\begin{align*} v_f &= v_i +at \\ 66.67 &= 0 +a(3) \\ a &= 22.22 \ \frac{m}{s^2} \end{align*} $$


Part (c)

The maximum velocity of rocket is, {eq}v_{max} = 290 \ \frac{m}{s} {/eq}

Let the time taken to reach the maximum velocity be, {eq}t_1 {/eq}

Applying the kinematics equation, we get, $$\begin{align*} v_{max} &= v_i +at_1 \\ 290 &= 0 +(22.22)t_1 \\ t_1 &= 13.05 \ s \end{align*} $$


Part (d)

Let the displacement of rocket when it reaches it's maximum velocity be, {eq}x_1 {/eq}

Applying the kinematics equation, we get, $$\begin{align*} x_1 &= (\dfrac{v_{max}+v_i}{2})t_1 \\ &= (\dfrac{290+0}{2})(13.05) \\ &= 1892.25 \ m \end{align*} $$


Learn more about this topic:

Loading...
Five Kinematics Quantities & the Big 5 Equations

from

Chapter 7 / Lesson 3
5.8K

Kinematic quantities are calculated using the 'big 5' equations that explain a motion in constant acceleration, when in a straight line. Learn each of these variables and how they fit into example calculations provided.


Related to this Question

Explore our homework questions and answers library