Question

A mysterious rocket-propelled object of mass 46.5 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude F(t) _________.

Answer 1

Question:

A mysterious rocket-propelled object of mass.. A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude  F(t) = (16.8N/s)t is applied. How far does the object travel in the first 5.00 s after the force is applied?

Answer:

The object travels 7.53 m in the first 5.00 s after the force is applied

Explanation:

Let the force F  be given by

F = ma

Where

m = Mass = 46.5 kg

a = Acceleration

We can express the force as a function of time as follows

F = pt

p = variable of F as a function of time

t = Time

Therefore a = pt/m

∴ $\frac{dv}{dt} = \frac{pt}{m}$

${dv} = \frac{pt}{m}dt$

${\int\limits^v_0 dv} =\int\limits^t_0 \frac{pt}{m}dt$

v = $\frac{pt^2}{2m}$

$\frac{dx}{dt}$=$\frac{pt^2}{2m}$

$dx = \frac{pt^2}{2m} dt$

$\int\limits^x_0 \, dx = \int\limits^t_0 \frac{pt^2}{2m} dt$

x = $\frac{pt^3}{6m}$

x =  Distance

After 5 seconds F = 16.8*5 = 84 N and

a = F/a = 1.8 m/s²  and

p = ma/t = 16.8 N/s

x = 16.8*5³÷(6*46.5)

= 7.53 m