In this page calculus application problem3 we are going to see solution of the second problem of the topic application problems in calculus.calculus application problem3

**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, we need to find the value of dx/dt for that we have to differentiate the given function with respect to "t".

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 by the fraction 3600/1000

= (20 x 3600)/1000

= 72 km/hr

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- 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