Question

A car is traveling around a banked curve without friction which is banked at 28 degrees. It is originally moving at 14 m/s. A constant acceleration of 2.5 m/s2 in the direction is applied in the direction that it is moving which causes the car to speed up. If this acceleration is applied for 2.7 seconds, how far did the car move up the road (the incline) in meters?

Answer 1

For frictionless banked road turning, the centripetal force is balanced by the the component of Normal reaction by the road. (R is the radius of the circle formed when the car is taking turn)

Now, when the car is moving at 14 m/s the value of r will be,

After acceleration of 2.5 m/s^2 for a time of 2.7 seconds the final velocity will be 20.75 m/s, then the value of r will be,

Now, to get the change in distance along the incline we have to divide this change in r with cos (here that change in r is adjacent side and distance along the incline is the hypotenuse for a triangle formed).

Therefore the distance car moves along the incline x, is,