**Word Problems Involving Rate of Change Worksheet :**

In this section, we will see some practice problems involving rate of change.

**Question 1 :**

A missile fired ground level rises x meters vertically upwards in t seconds and x = 100t - (25/2)t^{2}. 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.

**Question 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 v^{2 }Solution

**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)t^{2}

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.

**Question 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

**Question 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. Solution

**Question 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 Solution

**Question 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. Solution

**Question 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

**Question 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? Solution

We hope that the students would have understood how to solve word problems in rate of change.

If you need any other stuff, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**