An object moves in a circle with constant speed. The circle has a radius R and i
ID: 1329759 • Letter: A
Question
An object moves in a circle with constant speed. The circle has a radius R and is centered at the origin in the x-y plane. When the object is at the position (R, 0), which of the following statements is true about its acceleration vector? (a) The acceleration vector points in the +x direction. (b) The acceleration vector points in the x direction. (c) The acceleration vector points in the +y direction. (d) The acceleration vector points in the y direction. (e) The acceleration vector is zero.
3. A vector A~ is 5.50 m long and points west. A vector B~ is 3.00 m long and points south. What is the magnitude of the vector A~ B~ ? (a) 2.50 m (b) 4.61 m (c) 6.26 m (d) 8.50 m
4. (2 pts) An object has an x position as a function of time given by x(t) = (2.00 m/s 3 )t 3 (1.80 m/s)t. What is the x velocity at time t = 1.50 s? (a) 2.70 m/s (b) 4.05 m/s (c) 11.7 m/s (d) 18.0 m/s
5. A ball has an initial velocity of 5 m/s west. After some time, its velocity is 2 m/s north. What is the direction of the average acceleration of the ball during the time interval? (a) exactly north (b) exactly south (c) exactly east (d) exactly west (e) generally north east (f) generally north west (g) generally south east (h) generally south west
please explain each answer, i know the answers but am looking for explanations.
Explanation / Answer
2. (a) The acceleration vector points in the +x direction.
this is because the centripetal acceleration is towards the centre in the x direction.
3) A vector is in west direction,(5.5m)
-B would mean it will point to north (length = 3m)
magnitude = sqrt ( A2+B2) = sqrt ( 5.52+3.02)
=6.264 m (c)
4) x(t) = (2.00 m/s 3 )t3 (1.80 m/s)t.
velocity = dx/dt = 3*(2.00 )*t2 -1.8
so, velocity at t=1.5 secs = 3*(2.00 )*(1.5)2 -1.8 = 11.7 m/s
5) first of all the velocity decreases and changes direction from west to east.
this would mean that a deacceleration is a t work in the direction east to south .
so the answer will be (g) generally south east