Question

if velocity of an object is constant then displacement x varies with time t as

1) x ∝ t
2) x ∝ t^2
3) x ∝ t^3
4) x ∝ t^4​

Answer 1

Velocity is the rate of change of displacement .

v= dx/dt

Now ,it is  given that velocity is constant ,

dx=vdt

∴x ∝ t

displacement will be directly proportional to time.

Answer 2

Given info : The velocity of an object is constant.

To find : the displacement x varies with time t as ...

1. x ∝ t
2. x ∝ t²
3. x ∝ t⁴
4. x ∝ t⁴

solution : velocity is the rate of change of displacement with respect to time. in short, it is the change in the displacement in a specific time.

mathematically,

velocity is the first derivative of displacement function with respect to time.

i.e., v = $\bf{\frac{dx}{dt}}$ , where x denotes displacement.

∵ velocity of an object is constant.

∴ v = $\bf{\frac{dx}{dt}}$ = constant.

⇒$v\int\limits^t_0{dt}=\int\limits^x_0{dx}$

⇒vt = x

⇒x ∝ t

hence, the displacement of object x varies with time t as x ∝ t if velocity of it is constant. so the correct option is (1). x ∝ t