Answer:
1- The acceleration of the object is larger in magnitude the smaller the radius of the circle.
Explanation:
The acceleration of an object in a circular path is
As can be seen from the equation, if the radius of the circle is decreases, the magnitude of the acceleration increases.
As for the direction of the acceleration, it is always towards the center, and it is always perpendicular to the direction of the velocity.
(a) See graph in attachment
The appropriate graph to draw in this part is a graph of velocity vs time.
In this problem, we have a horse that accelerates from 0 m/s to 15 m/s in 10 s.
Assuming the acceleration of the horse is uniform, it means that the velocity (y-coordinate of the graph) must increase linearly with the time: therefore, the velocity-time graph will appear as a straight line, having the final point at
t = 10 s
v = 15 m/s
(b)
The average acceleration of the horse can be calculated as:
where
v is the final velocity
u is the initial velocity
t is the time interval
In this problem,
u = 0
v = 15 m/s
t = 10 s
Substituting,
(c) 75 m
For a uniformly accelerated motion, the distance travelled can be calculated by using the suvat equation:
where
s is the distance travelled
u is the initial velocity
t is the time interval
a is the acceleration
In this problem,
u = 0
t = 10 s
Substituting,
(d) See attached graphs
In a uniformly accelerated motion:
- The distance travelled (x) follows the equation mentioned in part c,
So, we see that this has the form of a parabola: therefore, the graph x vs t will represents a parabola.
- The acceleration is constant during the motion, and its value is
(calculated in part b)
therefore, the graph acceleration vs time will show a flat line at a constant value of 1.5 m/s^2.
