The distance x travelled by a body In a straight line is directly prop

1.	The distance x travelled by a body In a straight line is directly proportional to t2. Decide on the type of motion associated. If x ∝ t3 what change will you observe?
Answer» x ∝ t² = kt² where k is a constant a = ((d/dt)(dx/dt)) = (d/dt) (2 k t ) = 2 k ∴ Acceleration is constant/uniform. If x ∝ t³ where k is a constant a = ((d/dt)(dx/dt)) = (d/dt)(3 k t²) = 6 k t ∴ Acceleration is non-uniform

The distance x travelled by a body In a straight line is directly proportional to t2. Decide on the type of motion associated. If x ∝ t3 what change will you observe?

Answer»

x ∝ t² = kt² where k is a constant

a = ((d/dt)(dx/dt)) = (d/dt) (2 k t )

= 2 k

∴ Acceleration is constant/uniform.

If x ∝ t³ where k is a constant

a = ((d/dt)(dx/dt)) = (d/dt)(3 k t²) = 6 k t

∴ Acceleration is non-uniform