Question

A body of mass 0.40 kg moving initially with a constant speed of 10 m s–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.​

Answer 1

Step-by-step explanation:

Mass of the body, m = 0.40 kg

Initial speed of the body, u = 10 m/s due north

Force acting on the body, F = –8.0 N

Acceleration produced in the body, a = F / m = -8.0 / 0.40 = -20 ms-2

(i) At t = –5 s

Acceleration, a' = 0 and u = 10 m/s

s = ut + (1/2) a' t2

= 10 × (–5) = –50 m

(ii) At t = 25 s

Acceleration, a'' = –20 m/s2 and u = 10 m/s

s' = ut' + (1/2) a" t2

= 10 × 25 + (1/2) × (-20) × (25)2

= 250 - 6250 = -6000 m

(iii) At t = 100 s

For 0 ≤ t ≤ 30 s

a = -20 ms-2

u = 10 m/s

s1 = ut + (1/2)a"t2

= 10 × 30 + (1/2) × (-20) × (30)2

= 300 - 9000 = -8700 m

For 30 < t ≤ 100 s

As per the first equation of motion, for t = 30 s, final velocity is given as:

v = u + at

= 10 + (–20) × 30 = –590 m/s

Velocity of the body after 30 s = –590 m/s

For motion between 30 s to 100 s, i.e., in 70 s:

s2 = vt + (1/2) a" t2

= -590 × 70 = -41300 m

∴ Total distance, s" = s1 + s2 = -8700 -41300 = -50000 m = -50 km.

Answer 2

Mass of the body, m = 0.40 kg

Initial speed of the body, u = 10 m/s due north

Force acting on the body, F = –8.0 N

Acceleration produced in the body,

a = f/m = -8.0/0.40 = - 20 m/s^2

At t = –5 s

Acceleration, a' = 0 and u = 10 m/s

S = ut + 1/2 a' t^2 = 10× (-5)= -50 m

At t = 25 s

Acceleration, a'' = –20 m/s2 and u = 10 m/s

S' = ut' + 1/2 a'' t^2 = (10×25)+ 1/2 (-20)× (25)^2

= 250+ 6250= - 6000 m

At t = 100 s For 0≤ t ≤ 30

a = –20 m/s2

u = 10 m/s

S' = ut' + 1/2 a'' t^2 = (10×30)+ 1/2 (-20)× (30)^2

= 300- 9000 = - 8700 m

For 30≤ t ≤ 100

As per the first equation of motion,

for t = 30 s,

final velocity is given as:

v = u + at = 10 + (–20) × 30 = –590 m/s

Velocity of the body after 30 s = –590 m/s

For motion between 30 s to 100 s, i.e., in 70 s:

S' = ut' + 1/2 a'' t^2

= –590 × 70 = –41300 m

Total distance= -8700-41300 = -50000 m

I hope, this will help you☺✌✌