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**Linear Accelerated Motion Part 2**

For the Higher Level Leaving Cert Course ©Edward Williamson, Applied Maths Local Facilitator, Coachford College, Co Cork

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**Section 3 Vertical Motion**

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Gravity Signs are always how you start e.g. if you start throwing upwards, then up is + Acceleration is g and always down. Sign depends on if you say up is + or down is +. Watch for displacement e.g. throwing something off a cliff 30 m above ground, hence displacement is -30

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Example 3.1 [LC:1988 Q1 (b)] A particle falls freely from rest from a point o, passing three points a, b and c, the distances ab and bc being equal. If the particle takes 3 s to pass from a to b and 2 s from b to c, calculate |ab|

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**Always go from A as initial velocity remains same**

+ A u=u x A to C A to B B 2x u=u, a=g, s=x, t=3 u=u, a=g, s=2x, t=5 C Down is positive hence g is positive here Solve to give x =147 m

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Example 3.2 [LC:2002 Q1(a)] A stone is thrown vertically upwards under gravity with a speed of u m/s from a point 30 m above the horizontal ground. The stone hits the ground 5 s later. Find the value of u Find the speed with which it hits the ground.

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**Displacement is -30 because up is positive**

u=+u a=-g s=-30 t=5 + -30 Finding v Finding u

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Example 3.3 [LC:1990 Q1(a)] A particle is projected vertically upwards with velocity u m/s and is at a height h after t1 and t2 seconds respectively. Prove that:

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u=+u a=-g s=+h t=t (t1 on way up, t2 on way down) h Solving + Product of 2 roots Remember α and β

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Example 3.4 [LC:1992 Q1(a)] A balloon ascends vertically at uniform speed. 7.2 seconds after it leaves the ground, a particle is let fall from the balloon. The particle takes 9 seconds to reach the ground. Calculate the height from which the particle was dropped.

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Balloon + u h For the Particle u= +u a= -9.8 t= 9 s= -h

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Example 3.5 [LC:2007 Q1(a)]

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**Equations always give zero to n time**

3rd second is between t=2 seconds and t=3 seconds Equations always give zero to n time Let x = distance travelled in first 3 seconds Let y = distance travelled in first 2 seconds From the Question

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**Finding Height of the tower**

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**Now try some questions by yourself on the attached sheet**

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Kinematics. Topic Overview Kinematics is used to analyze the motion of an object. We use terms such as displacement, distance, velocity, speed, acceleration,

Kinematics. Topic Overview Kinematics is used to analyze the motion of an object. We use terms such as displacement, distance, velocity, speed, acceleration,

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