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

# The relation between the time t and position x for a particle moving on the x-axis is given by t=px2+qx, Where p and qare constants. The relation between velocity band acceleration a is as

A
aαv3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
aαv2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
aαv4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
aαv
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A aαv3The relation between the timet and position x for a particle moving on the x-axis is given byt=px2+gxDifferentiate with respect to time,dtdt=d(px2)dt+d(qx)dt1=2pxdxdt+qdxdt. . . .. .(1)We know that, velocity v=dxdtEquation (1) becomes1=2pxv+qvx=1−qv2pv. . . . . .(2)Differentiate with respect to time againd(1)dt=2pd(xv)dt+qdvdt0=2p(xdvdt+vdxdt)+qdvdt2p(xa+v.v)+qa=0 (a=dvdt)2pxa+2pv2+qa=02p1−qv2pva+2pv2+qa=0 (from equation 2)(1−qvv)a+qa=−2pv2a(1−qv+qv)=−2pv3a=−2pv3a∝v3The correct option is A.

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Displacement
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program