## Rate of Change Worksheet

In this page rate of change worksheet we are going to see some practice questions of the topic rate of change.

Definition

If a quantity y depends on and varies with quantity x the rate of change of y with respect to x is dy/dx.

In other words we can define rate of change as the ratio of the rate of change in input values and rate of change in output values.

 (1) A missile fired ground level rises x meters vertically upwards in t seconds and x = 100t- (25/2)t². Find (i) the initial velocity of the missile, (ii) the time when the height of the missile is a maximum (iii) the maximum height reached and (iv) the velocity with which the missile strikes the ground. Solution rate of change worksheet (2) A particle of unit mass moves so that displacement after t seconds is given by x = 3 cos (2t - 4). Find the acceleration and kinetic energy at the end of 2 seconds. (K.E = (1/2) m v² Solution (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 (4) Newton's law of cooling is given by θ = θ₀° e^(⁻kt), where the excess of temperature at zero time is θ₀° C and at time t seconds is θ° C. Determine the rate of change of temperature after 40 s ,given that θ₀ = 16° C and k = -0.03.(e^1.2 = 3.3201) Solution (5) The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm²/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm². (6) At noon, ship A is 100 km west of ship B. Ship A is sailing east at 35 km/hr and ship B us sailing north at 25 km/hr. How fast is the distance between the ship changing at 4.00 p.m (7) Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at the rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3. (8) Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of third side increasing when the angle between the sides of fixed length is 60°? Solution (9) Gravel is being dumped from a conveyor belt at a rate of 30 ft³/min and its coarsened such that it forms a pile in the shape of cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?

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