Question

When a car of mass 1167 kg accelerates from 10.0 m/s to some final speed, 4.00  10 5J of work are done. Find this final speed.

Answer 1

• Mass=1167kg
• Initial velocity=u=10m/s
• Acceleration=a=4m/s^2
• Work done=105J=W
• Final velocity=v=?
• Force=F
• Distance=d

Apply Newton's second law

$\\ \tt\hookrightarrow F=ma$

$\\ \tt\hookrightarrow F=1167(4)=4668N$

Now

$\\ \tt\hookrightarrow W=Fd$

$\\ \tt\hookrightarrow d=\dfrac{W}{F}$

$\\ \tt\hookrightarrow d=\dfrac{105}{4668}$

$\\ \tt\hookrightarrow d=0.022m$

Now

• d be s

According to third equation of kinematics

$\\ \tt\hookrightarrow v^2=u^2+2as$

$\\ \tt\hookrightarrow v^2=10^2+2(4)(0.022)$

$\\ \tt\hookrightarrow v^2=100+8(0.022)$

$\\ \tt\hookrightarrow v^2=100+0.176$

$\\ \tt\hookrightarrow v^2=100.176$

$\\ \tt\hookrightarrow v=10.001m/s$