Question

The velocity of a particle moving on the x-axis is given by v
= x2 + x where v is in m/s and x is in m. Find its acceleration
in m/s2 when passing through the point x = 2m
(a) 0
(b) 5
(c) 11
(d) 30​

Answer 1

Answer:

(d) 30

Step-by-step explanation:

a=dv/dt; Let us differentiate v(x):

 

dv/dt=dv/dx*dx/dt=dv/dx*v, since dx/dt is velocity itself. I used a chain rule here, as you may notice.

 

dv/dx is given by:

 

dv/dx=2x+1; Thus we obtain:

 

a=dv/dt=(2x+1)*v(x)=(2x+1)*(x2+x)=2x3+3x2+x

 

Now all you have to do is to plug in x=2

 

a(x=2 m)=2*23+3*22+2=16+12+2=30 m/s2

Answer 2

Answer:

D

Step-by-step explanation:

a=dv/dt; Let us differentiate v(x):

dv/dt=dv/dx*dx/dt=dv/dx*v, since dx/dt is velocity itself. I used a chain rule here, as you may notice.

dv/dx is given by:

dv/dx=2x+1; Thus we obtain:

a=dv/dt=(2x+1)*v(x)=(2x+1)*(x2+x)=2x3+3x2+x

Now all you have to do is to plug in x=2

a(x=2 m)=16+12+2=30 m/s2