Question

The velocity of a particle moving in a straight line is given by v = t(t²+2)²+t .

Find an expression for the position s after a time t. ( Use C for the constant of intergation.)

Answer 1

To find the expression for the position s after a time t, integrate the given velocity function with respect to time.

Step-by-step explanation:

To find the expression for the position s after a time t, we need to integrate the given velocity function with respect to time. Let's start by integrating each term separately.

∫t(t²+2)² dt = ∫(t⁴ + 4t³ + 4t²) dt = (1/5)t⁵ + (1/3)t⁴ + (4/3)t³ + C

∫t dt = (1/2)t² + C'

Combining these integrals, we get the expression for the position as:

s = (1/5)t⁵ + (1/3)t⁴ + (4/3)t³ + (1/2)t² + t + C + C'