Department of Mechanical Engineering, KNUST
ME 261 Dynamics of Solid Mechanics
Assignment 1&2
Due: 25th September, 2018 at 12:00 noon
1. The motion of a particle is defined by the relation x=0.5t3 -15t2 +10t+8, where x and t
are expressed in m and s, respectively. Determine the position, the velocity, and the
acceleration of the particle when t=4 s.
2. The motion of a particle is defined by the relation x= 4t4 -2t3 -8t2 + 3t + 3, where x and
t are expressed in metres and seconds, respectively. Determine the time, the position,
and the velocity when a =0.
3. The motion of a particle is defined by the relation x = t3 -6t2 - 36t-40, where x is
expressed in meters and t in seconds. Determine (a) when the velocity is zero, (b) the
corresponding the position and acceleration.
4. A motorcyclist travels along a straight road at a speed of 27 m/s. When the brakes are
applied, the motorcycle decelerates at a rate of -6t m/s2. Find the distance the
motorcycle travels before it stops.
5. A particle has an initial velocity of 3 m/s to the left at initial position s0 = 0 Determine
its position when t = 3 s if the acceleration is 4 m/s 2 to the right.
6. A projectile is fired from the edge of a 150-m cliff with an initial velocity of 180 m/s at
an angle of 30° with the horizontal. Neglecting air resistance, find (a) the horizontal
distance from the gun to the point where the projectile strikes the ground, (b) the
greatest elevation above the ground reached by the projectile.
7. An airplane used to drop water on brushfires, as shown in Figure P1.7, is flying
horizontally in a straight line at 315 km/h at an altitude of 80 m. Determine the distance
d at which the pilot should release the water so that it will hit the fire at B.
Figure P1.7
Figure P1.8
8. In Figure P.8, the golf ball is hit at A with a speed of VA = 40 m/s and directed at an
angle of 30° with the horizontal as shown. Determine the distance d where the ball
strikes the slope at B.
9. Two vehicles are approaching each other in the same lane. At time t = 0, vehicles A and B are
at a distance of d apart and their approaching speeds are uA and uB, respectively. To avoid
collision drivers of both vehicles step on their brakes at the same time and the two vehicles
stopped just before collision at time t with constant retardations a A and a B .
a. Show that t =
2d
u A + uB
b. Find a A in terms of u A , u B and d.
10. A car is travelling at speed of 15 m/s and acceleration of 6 m/s 2 on a curved road of
radius 50 m. Calculate the magnitude of the acceleration of the car