The equation for the change of position of a train starting at x = 0 m is given by $x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }$ .The dimensions of b are A)T ^- ³ B)LT ^- ³ C)LT ^- ² D)LT ^- ¹ E)L ^- ¹T ^- ¹

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The equation given is: x(t) = b(1 - e^(-0.3t)) The dimensions of x(t) must be length (L). The dimensions of time (t) must be time (T). Therefore, the dimensions of b must be: L / (1 - e^(-0.3t)) Simplifying, we get: L / (1 - e^(-0.3T)) This is best represented by option B: LTF1F1F1S1^-F1F1F10³

The Equation for the Change of Position of a Train x=12at2+bt3x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }x=21​at2+bt3

The Equation for the Change of Position of a Train $x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }$