Question

a particle moving in a straight line with initial velocity u and uniform acceleration a. if the sum of the distance travelled in t th and (t+1) th second is 100cm. then find the velocity after t seconds in cm/s​

Answer 1

v=u+a*t

Thus d(t)=u*t+0.5*a*t^2

d(t+1)=u*(t+1)+0.5*a*(t+1)^2

Thus d(t+1)+d(t)=u*(t+1)+0.5*a*(t+1)^2-+u*t+0.5*a*t^2]

=u*(2t+1)+0.5*a*[2t+1]=(2t+1)[u+a*t]…………….1

As sum dist. traveled in t to(t+1)=100

=u*t+0.5*a*[2t+1]=100

v(t)=u+a*t

From1,

v(t)=100/2t+1 cm/sec