Question

A particle is starting from rest and moving with a constant acceleration 'a'. The ratio of the distances travelled in the first second, third and fourth seconds is

a) 1:4:9:16
b) 1:1:1:3
c) 1:2: 3:4
d) 1:3:5:7
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Answer 1

Answer:

c) 1:2: 3:4

Explanation:

The formula for the distance travelled by a particle with constant acceleration can be expressed as:

distance = initial velocity * time + 0.5 * acceleration * time^2

Since the particle is starting from rest (initial velocity = 0), the formula can be simplified to:

distance = 0.5 * acceleration * time^2

The ratio of distances travelled in the first, third, and fourth seconds can be calculated as:

distance travelled in 1 second = 0.5 * acceleration * 1^2 = 0.5 * acceleration

distance travelled in 3 seconds = 0.5 * acceleration * 3^2 = 4.5 * acceleration

distance travelled in 4 seconds = 0.5 * acceleration * 4^2 = 8 * acceleration

The ratio of these distances is:

distance travelled in 1 second : distance travelled in 3 seconds : distance travelled in 4 seconds = 0.5 * acceleration : 4.5 * acceleration : 8 * acceleration = 1 : 3 : 4

Therefore, the ratio of the distances travelled in the first second, third and fourth seconds is 1:2:3:4.

Answer 2

Answer:

solution: option d)1:3:5:7