Question

A balls rolls down an inclined track 2 m long in 4 s. Find (1) Acceleration (2) Time taken to cover the second metre of the track and (3) Speed of the ball at the bottom of the track

Answer 1

Answer:

1) Acceleration = 0.25 m/s²

2) Time taken to cover the second metre of the track = 1.17 sec

3) speed of the ball at the bottom of track = 1m/s

Step-by-step Explanations :

Given : length of inclined track = 2m

Time taken = 4 sec

To find : 1) Acceleration,

2) Time taken to cover the second metre of the track and ,

3) Speed of the ball at the bottom of the track

Given values,

Length of inclined track (l) = 2m

Time taken to roll down the inclined (t) = 4 sec

Initial velocity (u) = 0

Using the equation of motion along the incline plane,

s = ut + 1/2 × at²

Substituting the given value in above formula we get,

2 = 0 + 1/2 × a × (4)²

2 = 1/2 × 16a

2 = 8a

a = 2/8 = 0.25 m/s²

Now, for the ball to cover 1 m distance along the incline plane,

s = ut + 1/2 × at²

Substituting the given value in above formula we get,

1 = 0 + 1/2 × (0.25)×(t1)²

∴ t1 = √8 sec

Now, for the ball to cover 2 m distance along the incline from the start ,

s = ut + 1/2 × at²

Substituting the given value in above formula we get,

2 = 0 + 1/2 × (0.25)×(t2)²

∴ t2 = 4 sec

The time taken to cover the second meter is T = t2 - t1

T = 4 - √8

= 1.17 sec

Using the first equation of motion,

v = u + at

Substituting the given value in above formula we get,

v = 0 + 0.25 × 4

v = 1 m/s