# The equation of motion of an object is x=3+7t-8t^2. What is the velocity of the object at the time t=2.5 s?

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Expert Answers

justaguide | Certified Educator

The displacement of the object is given by x = 3 + 7t - 8t^2.

The velocity is the first derivative of the expression for the displacement with respect to time.

v = `dx/dt ` = (3 + 7t - 8t^2)'

=> 0 + 7 - 16t

At t = 2.5, the velocity is 7 - 16*2.5 = -33

**The velocity of the object at time t = 2.5 is -33 units/s^2.**

Student Comments

imaankasana | Student

x=3+7t-8t^2

taking derivative w.r.t t on both sides of eq

dx/dt=d/dt (3+7t-8t^2)

as v=dx/dt

so v=0+7-8(2)t

v=7-16t

given that t=2.5sec

v=7-16(2.5)

v=7-40

v=-33m/sec