Question

Force of magnitude 8 Newton acting on a body changes its velocity from 10 metre per second to 30 metre per second distance of hundred metres find the mass and the time taken by the body

Answer 1

Answer:

mass=2kg and time=5sec

Answer 2

Answer:

Mass of the body is 2 kg

Time taken by the body is 5 seconds

Explanation:

Provided that:

Force applied (F) = 8 N

Initial velocity (u) = 10 m/sec

Final velocity (v) = 30 m/sec

Distance moved during this velocity change (s) = 100 m

Now let's consider the mass of the body = m kg

And acceleration due to applied force = a m/sec^2

From Kinematics we know;

${v}^{2} = {u}^{2} + 2as \: \: ...equation(i)$

So putting the values of v, u and s we get the acceleration (a);

${v}^{2} = {u}^{2} + 2as \\ a = \frac{( {v}^{2} - {u}^{2} )}{2s} \\ a = \frac{ ({30}^{2} - {10}^{2}) }{(2 \times 100)} \: m. {sec}^{ - 2} \\ a = 4 \: m. {sec}^{ - 2}$

So the acceleration is 4 m/sec^2

Hence, we get the mass of the body;

$F = m.a \: \: ...equation(ii) \\ or \: m= \frac{F}{a} \\ or \: m = \frac{8}{4} \:kg \\ or \: m = 2 \: kg$

Hence the mass of the body is 2 kg

Now,

$v = u + at \: \: ...equation(iii) \\ or \: t = \frac{(v - u)}{a} \\ or \: t = \frac{(30 - 10)}{4} \: sec \\ or \: t = 5 \: sec$

Hence the time needed to reach the velocity from 10 m/sec to 30 m/sec is 5 seconds.