Practice Problems on Equation of Motion by Calculus Method
Q1. A car moves along a straight road with its position given by s(t)=2t2-5t+3, where s is in metres and t is in seconds. Determine the car’s velocity and acceleration at time t =3s.
Q2. The height of a ball thrown upwards is given by h(t)=3.5t-4.9t2, find its velocity and acceleration as a function of time. Also, find the maximum height reached by the ball.
Q3. A particle is moving along the y-axis, and its velocity is given by v(t)= 2t2-3t+5 m/s. Find its displacement between t =1 second and t =4 seconds.
Q4. An object is dropped from a height of 100 metres. Its velocity function as it falls is given by v(t)=9.8t, where t is the time in seconds and v is in metres per second. Determine the height of the object after the first 5 seconds of its fall.
Q5. A car accelerates with an acceleration function a(t)=2t2−3 m/s². Calculate the displacement of the car from t=0 to t=6 seconds.
Equation of Motion by Calculus Method
In Physics, Motion is the state of body in which it changes its position with time. Motion is fundamentally described by physical quantities such distance, displacement, speed, velocity, acceleration, and time. These physical quantities can be expressed in the form of a mathematical equation to express motion. These equations are called Equations of Motion. These equations can be derived via various methods such as Algebraic Method, Graphical Method and Calculus Method.
This article deals with the equation of motion and its derivation using the calculus method. This derivation is useful for class 11 students.
Table of Content
- Fundamentals of Motion
- Equations of Motion by Calculus Method
- Applications of Calculus in Motion
- Examples on Equation of Motion by Calculus Method
- Practice Problems on Equation of Motion by Calculus Method
- Conclusion: Equation of Motion by Calculus Method