Q2. (a) A bike is moving in straight line along x-axis with uniform speed with x-component...

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Q2. (a) A bike is moving in straight line along x-axis with uniform speed with x-component of velocity given by (3+A) . Calculate the distance along x-axis traveled from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1 is v1=(3+A)m/s. (b) A bike is accelerating in straight line along x-axis acceleration given by (2+A)*t². Calculate the distance traveled along x-axes from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1=(3+A)s is v1=(4+A)m/s. (c) A bike is accelerating along a curve in xy- plane. Its acceleration along different components is given by a=(3+A)*t² and a,= (1+A)*t². Calculate the distance traveled along xy- plane from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1 is v1=(2+A)m/s along x-axis and v1=(1+A)m/s at time t1 along y-axis Linear Vector Analysis Q1. Given following operators find out if they are linear or not. (a) A==(b)B(c)=c² Q2. Given following linear operators find out if they are eigen-operators or not corresponding (a) A (Operator)=f(x)=e³ (3+R)x 2,f(x) = cos(x+R) (c) B=+R,f(x)=sin(x+R) dx²¹ b) B=_d² dx² Q2. (a) A bike is moving in straight line along x-axis with uniform speed with x-component of velocity given by (3+A) . Calculate the distance along x-axis traveled from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1 is v1=(3+A)m/s. (b) A bike is accelerating in straight line along x-axis acceleration given by (2+A)*t². Calculate the distance traveled along x-axes from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1=(3+A)s is v1=(4+A)m/s. (c) A bike is accelerating along a curve in xy- plane. Its acceleration along different components is given by a=(3+A)*t² and a,= (1+A)*t². Calculate the distance traveled along xy- plane from time t1=(2+A)s to t2=(5+A)s. The speed of bike at time t1 is v1=(2+A)m/s along x-axis and v1=(1+A)m/s at time t1 along y-axis Linear Vector Analysis Q1. Given following operators find out if they are linear or not. (a) A==(b)B(c)=c² Q2. Given following linear operators find out if they are eigen-operators or not corresponding (a) A (Operator)=f(x)=e³ (3+R)x 2,f(x) = cos(x+R) (c) B=+R,f(x)=sin(x+R) dx²¹ b) B=_d² dx²