Question

the distance covered by a car at a time t is given by x=20t+6t^4. calculate the instantaneous velocity and acceleration when t= 1s.​

Answer 1

t = 1s is 44 m/s and 72 m/s^2

Step-by-step explanation:

The distance covered by a car at a time t is given by x=20t+6t^4. To calculate the instantaneous velocity and acceleration when t=1s, we can use the formulas for velocity and acceleration, which are:

Velocity (v) = dx/dt = d/dt(20t+6t^4) = 20 + 24t^3

Acceleration (a) = dv/dt = d/dt(20 + 24t^3) = 72t^2

When t = 1s, we can substitute this value into the formulas for velocity and acceleration:

Velocity (v) = 20 + 24(1)^3 = 20 + 24 = 44 m/s

Acceleration (a) = 72(1)^2 = 72 m/s^2

Therefore, the instantaneous velocity and acceleration of the car when t = 1s is 44 m/s and 72 m/s^2, respectively.