• 9 Questions
Calculate the area of the plane region bounded by the curve and the -axis.
The plan view of a single corridor floor is bounded by lines , and the curve , all measured in metres. What is the cost of covering 3 such corridors with granite at the price of 100 pounds per square metre?
Find the area of the region bounded by the curves and .
Find the area of the region enclosed by the curves and and the lines and .
A particle’s velocity in metres per second as a function of time is . What distance does it travel between and ?
• 10 Questions
A particle moves along the positive axis, starting at . It’s acceleration varies directly with , where is the time in seconds. At , the particle’s displacement is 10 m, and its velocity is 20 m/s. Express the particle’s displacement, , and its velocity, , in terms of .
A particle is moving in a straight line such that its acceleration, meters per second squared, and displacement, meters, satisfy the equation . Given that the particle's velocity was 31 m/s when its displacement was 0 m, find an expression for in terms of , and determine the speed that the particle approaches as its displacement increases.
A particle started moving from a fixed point in a straight line such that its acceleration , measured in metres per second squared, and its position , measured in metres, satisfy the following equation: . Given that the initial velocity of the particle was 8 m/s, find an expression for in terms of .
A particle is moving in a straight line such that its acceleration at time seconds is given by Given that its initial velocity is 15 m/s, find an expression for its displacement in terms of .
A particle moves along the axis, starting at the origin with initial velocity 13 m/s. After a time seconds, the acceleration is given by Find , the particle’s displacement at time seconds, and determine its displacement, , when its velocity is 16 m/s.