Problem 1 :
The distance x metres described by a car in time t seconds is given by :
x = 3t^{3} - 2t^{2} + 4t - 1
Determine the velocity and acceleration when
(i) t = 0 and
(ii) t = 1.5 s
Solution :
Problem 2 :
The angular displacement θ radians of a fly wheel varies with time t seconds and follows the equation
θ = 9t^{2} - 2t^{3}
Determine (i) the angular velocity and acceleration of the fly wheel when time t = 1 second and (ii) the time when the angular acceleration is zero.
Solution :
Problem 3 :
Supplies are dropped from an helicopter and distance fallen in time t seconds is given by
x = (½)gt^{2}
where g = 9.8 m/sec^{2}. Determine the velocity and acceleration of the supplies after it has fallen for 2 seconds.
Solution :
Problem 4 :
A missile fired from ground level rises x meters vertically upwards in t seconds and
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 :
Problem 5 :
A boy, who is standing on a pole of height 14.7 m throws a stone vertically upwards. It moves in a vertical line slightly away from the pole and falls on the ground. Its equation of motion in meters and seconds is
x = 9.8t - 4.9t^{2}
(i) Find the time taken for upward and downward motions.
(ii) Also find the maximum height reached by the stone from the ground.
Solution :
Derivative Problems and Solutions (Part - 1)
Derivative Problems and Solutions (Part - 2)
Derivative Problems and Solutions (Part - 3)
Derivative Problems and Solutions (Part - 4)
Derivative Problems and Solutions (Part - 5)
Derivative Problems and Solutions (Part - 6)
Derivative Problems and Solutions (Part - 7)
Derivative Problems and Solutions (Part - 8)
Derivative Problems and Solutions (Part - 9)
Derivative Problems and Solutions (Part - 10)
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