1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The velocity of a particle is at any time related to the distance travelled by the particle by the relation v=ax+b, where a is positive and b ≤a2. Which of the following statements will be true for this motion? (given x = 0 when t = 0)

A
The displacement of the particle at time t is x=ba(eat1)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
The particle will experience a retardation if b < 0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
The particle will be at rest at time t = 0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
The motion of the particle is under constant acceleration.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B The particle will experience a retardation if b < 0v=ax+b;where a→+ve and b≤a2 dxdt=ax+b⇒∫dxax+b=∫dt ⇒ln(ax+b)a=t+c (1) given at t = 0, x = 0, ln(b)a=c put in(1) ∴ln(ax+b)a=t+ln(b)a ⇒1aln(ax+bb)=t ⇒ax+bb=eat ⇒x=ba(eat−1) and, v=ax+b=a(ba(eat−1))+b=beat acceleration=abeat ∴For b<0, acceleration will be negative i.e., particle will experience retardation v=ax+b=beat at t = 0, v = b i.e., not at rest. acceleration =abeat acceleration is varying with time

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program