Question

help!!!

A remotely controlled toy car travels along a straight line and its position changes with time following the law: X(t) = 20 - 3t + 5t" where the coefficients have such dimensions that the position X(t) is measured in meters, 12. What is the dimension of the coefficient, which has the numeric value of 5? 13. What is the initial position of the toy car at t-0s? 14. What is the initial velocity of the car at t-os? 15. What will be the position of the car at t-1 ? 16. What will be the instantaneous velocity of the car at this moment (ie, at the t=1s 17. What is the instantaneous acceleration of the car at t=1 s?!

Answer 1

12. the dimensions of the coefficient 5 in the equation for X(t) is,

Unit = m/s⁴

thus dimensions = [M¹L°T^-4]

13. initial position of the toy car

X(0) = 20 - 0

X(0) = 20 meters

14. for initial velocity,first we have to find the derivative of X(t),

V(t) = dX(t)/dt

V(t) = 20t³ - 3

Now velocity at t = 0 second

V(0) = -3 m/s

15. position of the car at t=1 second

X(1) = 20 - 3*(1) + 5*(1)⁴

X(1) = 22 m

16. Instantaneous velocity at t = 1 second,

V(1) = 20*(1)³ - 3

V(1) = 17 m/s

17. Acceleration is the derivative of velocity so,

a(t) = dV(t)/dt

a(t) = 60t²

Now the instantaneous acceleration at t =1 second

a(1) = 60 m/s²

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