Question

A particle starts from x = 0 and moves along a straight line such that its velocity v depends on position as
v=x + 4.For the first four seconds, average speed of the
particle in m/s) is
a) e^4+1
b) e^4-1
c) e^4+4
d) e^4-4​

Answer 1

Explanation:

Answer

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Correct option is

A

Magnitude of average velocity is 35 m/s

B

Average speed is 513 m/s

D

Average acceleration is −1 m/s2

Average velocity =ΔtS=Vavg

Displacement, S=∫05vdt=∫05(4t−t2)dt=325m

Vavg=5sec.25/3m=35secm

Now,

v=0att=4s

And after 4s the direction of velocity changes

∴Average speed =time takendistance covered=Δtdistance

Distance =∫04vdt+∫45(−v)dt

=3

Displacement, S=∫05vdt=∫05(4t−t2)dt=325m

Vavg=5sec.25/3m=35secm

Now,

v=0att=4s

And after 4s the direction of velocity changes

∴Average speed =time takendistance covered=Δtdistance

Distance =∫04vdt+∫45(−v)dt

=332+37=339m=13m

Average speed =513m/s

Average acceleration