A speedboat starts from rest and accelerates at +2.01m/s 2 for 7.20 s. At the en

Question

A speedboat starts from rest and accelerates at +2.01m/s2 for 7.20 s. At the end ofthis time, the boat continues for an additional 6.25 s with an acceleration of +0.518 m/s2.Following this, the boat accelerates at -1.49 m/s2 for8.50 s. (a) What is the velocity of the boat att = 21.95 s?
1 m/s

(b) Find the total displacement of the boat.
2 m

Section 2.4 Equations of Kinematics forConstant Acceleration
Section 2.5 Applications of the Equations ofKinematics
(a) What is the velocity of the boat att = 21.95 s?
1 m/s

(b) Find the total displacement of the boat.
2 m
Section 2.4 Equations of Kinematics forConstant Acceleration
Section 2.5 Applications of the Equations ofKinematics

Explanation / Answer

The speedboat starts from rest,that is,u = 0 m/s The speedboat accelerates at a1= +2.01m/s2 for time t1= 7.20s At the end of this time,the boat accelerates at a2=+0.518 m/s2 for time t2= 6.25s Following this, the boat accelerates at a3= -1.49m/s2 for t3= 8.50s (a)The speed of the boar when it accelerates for timet1= 7.20s is v1= u + a1t1 or v1= a1t1= 2.01 * 7.20 =14.472 m/s Similarly,we have v2= v1 +a2t2 or v2= 14.472 + 0.518 * 6.25 = 14.472 + 3.2375 =17.7095 m/s and v3= v2 +a3t3 or v3= 17.7095 + (-1.49 * 8.50) = 5.0445 m/s The distance travelled by the boat during time t1is S1= ut1 +(1/2)a1t12 =(1/2)a1t12 = (1/2) * 2.01 *(7.20)2 = 52.1 m Similarly,we have S2= v1t2 +(1/2)a2t22 or S2= 14.472 * 6.25 + (1/2) * 0.518 *(6.25)2 or S2= 100.57 m and S3= v2t3 +(1/2)a3t32 or S3= 17.7095 * 8.50 + (1/2) * (-1.49) *(8.50)2 or S3= 96.7 m Therefore,the velocity of the boat at t = 21.95 s is v4= (S1 + S2 +S3/t) or v4= (52.1 + 100.57 + 96.7/21.95) = 11.36m/s (b)The total displacement of the boat is S = S1 + S2 + S3 = 52.1 +100.57 + 96.7 = 249.37 m or S3= 96.7 m Therefore,the velocity of the boat at t = 21.95 s is v4= (S1 + S2 +S3/t) or v4= (52.1 + 100.57 + 96.7/21.95) = 11.36m/s (b)The total displacement of the boat is S = S1 + S2 + S3 = 52.1 +100.57 + 96.7 = 249.37 m

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