The maximum velocity it attains is 39.1 m/s
The velocity is changing over the course of time. Velocity is the rate of motion in a specific direction. Whereas acceleration is the rate of change of velocity of an object with respect to time. Maximum velocity is reached when you stop accelerating, To calculate velocity using acceleration, we start by multiplying the acceleration by the change in time
The acceleration of a motorcycle:
where [tex]a = 1.50 \frac{m}{s^{3}}[/tex] and [tex]ax* (t) = at - b*t^{2}[/tex]
[tex]a = 0.120 \frac{m}{s^{4}}[/tex]
The motorcycle is at rest at the origin at time t=0.
The maximum velocity it attains = ?
Answer:
[tex]v(t) = (1/2)At^2 - (1/3)Bt^3 v(0)[/tex]
but v(0) = 0.
[tex]x(t) = (1/6)At^3 - (1/12)Bt^4 x(0)[/tex]
but x(0) = 0.
[tex]v(t) = (0.75 \frac{m}{s^{3}}) t^2 - (0.04 \frac{m}{s^{4}})t^3[/tex]
Next step is find its position as a function of time.
[tex]x(t)= x(t) = (0.25 \frac{m}{s^{3}})t^3 - (0.01 \frac{m}{s^{4}})t^4[/tex]
Then, calculate the maximum velocity it attains.
Max velocity will be attained when
[tex]At = Bt^2[/tex]
T= 1.50/0.120 = 12.5 seconds
V(t) = 0.750(12.5)^2 – 0.04(12.5)^3 = 39.1 m/s
Grade: 9
Subject: physics
Chapter: the maximum velocity
Keywords: the maximum velocity
