Question

A rocket driven sled running on a straight, level track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of 1600 km/hin 1.8 s, starting from rest. Find (a)the acceleration (assumed constant) in terms of g(b) the distance traveled.

Short answer

1. The acceleration of the sled is 25 g .
2. The distance traveled by the sled is 400 m .

Step-by-step solution

Given information

$$\begin{gathered} v_f=1600\mathrm{km}/\mathrm{h} \\ =444.44\mathrm{m}/\mathrm{s} \\ t=1.8\mathrm{s} \end{gathered}$$

To understand the concept of kinematic equation of motion

The problem deals with the kinematic equation of motion. Kinematics is the study of how a system of bodies moves without taking into account the forces or potential fields that influence motion. The equations which are used in the study are known as kinematic equations of motion.

Formula:

The final velocity is given by,

$v_f=v_0+at$

The displacement is given by,

$x=\left(v_0\right)\left(t\right)+\frac{1}{2}a{t}^2$

a): Calculation for acceleration

According to the kinematic equations,

$$\begin{gathered} v_f=v_0+at \\ 444.44=0+a\left(1.8\right). \\ a=\frac{246.9}{9.8}\frac{\mathrm{m}}{{\mathrm{s}}^2} \\ =25.19 \\ ~25g \end{gathered}$$

Hence, the acceleration of sled would be $25g$.

a): Calculation for distance traveled by the sled

According to the kinematic equations,

$$\begin{gathered} x=\left(v_i\right)\left(t\right)+\frac{1}{2}a{t}^2 \\ x=\frac{1}{2}\left(246.9\right){\left(1.8\right)}^2 \\ x=400\mathrm{m} \end{gathered}$$

So, the distance traveled by the sled would be 400 m