The displacement, x m, of a particle from a fixed point O at time t s is given by x= t^4 -4(t)^3-8(t)^2+1 Find the total distance travelled by the particle during the first 5 seconds of motion???
The displacement, x m, of a particle from a fixed point O at time t s is given by x= t^4 -4(t)^3-8(t)^2+1 Find the total distance travelled by the particle during the first 5 seconds of motion???
Total distance travelled is the total area between the velocity graph and the time axis, when plotted against velocity-time axes.
OK, ignore that, I meant to say that you're looking for the total area between v(t)=dtdx graph and the time axis on a velocity-time graph.
So, you need to consider ∫v(t).dt (which you don't need to evaluate), but note that v(t) is -ve between t=0 and t=4 and positive between t=4 and t=5 therefore you need to make your area between t=0 and t=4 +ve before adding it onto the area from t=4 to t=5
So, the total distance traveled is just D=∫45v(t).dt−∫04v(t).dt=[x(t)]45−[x(t)]04