In this page rate of change question3 we are going to see solution of some practice question of the worksheet.

**Question 3:**

The distance x meters traveled by a vehicle in time t seconds after the brakes are applied is given by x = 20 t - (5/3)t². Determine

(i) the speed of the vehicle (in km/hr) at the instant the brakes are applied and

(ii) the distance the car traveled before it stops.

**Solution:**

the distance x meters traveled by a vehicle in time t seconds

x = 20 t - (5/3)t²

to find the speed of the vehicle

dx/dt = 20 (1) - (5/3)(2t)

= 20 - (10 t/3)

the speed of the vehicle (in km/hr) at the instant the brakes are applied

t = 0

= 20 - (10(0)/3)

= 20 - 0

velocity at t = 0

= 20 meter/seconds

to find velocity after the brakes are applied

= 20 meter/seconds

to convert this into km/hr we have to multiply it with the fraction 3600/1000

= (20 x 3600)/1000

= 72 km/hr

- Back to worksheet
- First Principles
- Implicit Function
- Parametric Function
- Substitution Method
- logarithmic function
- Product Rule
- Chain Rule
- Quotient Rule
- Rolle's theorem
- Lagrange's theorem
- Finding increasing or decreasing interval
- Increasing function
- Decreasing function
- Monotonic function
- Maximum and minimum
- Examples of maximum and minimum